Tool CaT
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | Der95 07 |
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stdout:
YES(?,O(n^1))
Problem:
w(r(x)) -> r(w(x))
b(r(x)) -> r(b(x))
b(w(x)) -> w(b(x))
Proof:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {3,2}
transitions:
r1(11) -> 12*
r1(8) -> 9*
b1(10) -> 11*
w1(7) -> 8*
w0(1) -> 2*
r0(1) -> 1*
b0(1) -> 3*
1 -> 10,7
9 -> 8,2
12 -> 11,3
problem:
QedTool IRC1
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | Der95 07 |
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stdout:
YES(?,O(n^1))
Tool IRC2
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | Der95 07 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: innermost runtime-complexity with respect to
Rules:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ w_0(2) -> 1
, w_1(2) -> 3
, r_0(2) -> 2
, r_1(3) -> 1
, r_1(3) -> 3
, b_0(2) -> 1
, b_1(2) -> 3}Tool RC1
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
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Input | Der95 07 |
---|
stdout:
YES(?,O(n^1))
Tool RC2
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | Der95 07 |
---|
stdout:
YES(?,O(n^1))
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
Proof Output:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the best result:
Details:
--------
'Bounds with minimal-enrichment and initial automaton 'match'' succeeded with the following output:
'Bounds with minimal-enrichment and initial automaton 'match''
--------------------------------------------------------------
Answer: YES(?,O(n^1))
Input Problem: runtime-complexity with respect to
Rules:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
Proof Output:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ w_0(2) -> 1
, w_1(2) -> 3
, r_0(2) -> 2
, r_1(3) -> 1
, r_1(3) -> 3
, b_0(2) -> 1
, b_1(2) -> 3}Tool pair1rc
Execution Time | Unknown |
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Answer | YES(?,O(n^1)) |
---|
Input | Der95 07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair1 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ w_0(2) -> 1
, w_1(2) -> 4
, r_0(2) -> 2
, r_1(4) -> 1
, r_1(4) -> 4
, r_1(5) -> 3
, r_1(5) -> 5
, b_0(2) -> 3
, b_1(2) -> 5}
Hurray, we answered YES(?,O(n^1))Tool pair2rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | Der95 07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair2 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ w_0(2) -> 1
, w_1(2) -> 4
, r_0(2) -> 2
, r_1(4) -> 1
, r_1(4) -> 4
, r_1(5) -> 3
, r_1(5) -> 5
, b_0(2) -> 3
, b_1(2) -> 5}
Hurray, we answered YES(?,O(n^1))Tool pair3irc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | Der95 07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ w_0(2) -> 1
, w_1(2) -> 3
, r_0(2) -> 2
, r_1(3) -> 1
, r_1(3) -> 3
, b_0(2) -> 1
, b_1(2) -> 3}
Hurray, we answered YES(?,O(n^1))Tool pair3rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | Der95 07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'pair3 (timeout of 60.0 seconds)':
-------------------------------------------------
The processor is not applicable, reason is:
Input problem is not restricted to innermost rewriting
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: none
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with perSymbol-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ w_0(2) -> 1
, w_1(2) -> 4
, r_0(2) -> 2
, r_1(4) -> 1
, r_1(4) -> 4
, r_1(5) -> 3
, r_1(5) -> 5
, b_0(2) -> 3
, b_1(2) -> 5}
Hurray, we answered YES(?,O(n^1))Tool rc
Execution Time | Unknown |
---|
Answer | YES(?,O(n^1)) |
---|
Input | Der95 07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: none
Certificate: YES(?,O(n^1))
Application of 'rc (timeout of 60.0 seconds)':
----------------------------------------------
'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match' (timeout of 100.0 seconds)' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ w_0(2) -> 1
, w_1(2) -> 3
, r_0(2) -> 2
, r_1(3) -> 1
, r_1(3) -> 3
, b_0(2) -> 1
, b_1(2) -> 3}
Hurray, we answered YES(?,O(n^1))Tool tup3irc
Execution Time | 7.13439e-2ms |
---|
Answer | YES(?,O(n^1)) |
---|
Input | Der95 07 |
---|
stdout:
YES(?,O(n^1))
We consider the following Problem:
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: innermost
Certificate: YES(?,O(n^1))
Application of 'tup3 (timeout of 60.0 seconds)':
------------------------------------------------
The input problem contains no overlaps that give rise to inapplicable rules.
We abort the transformation and continue with the subprocessor on the problem
Strict Trs:
{ w(r(x)) -> r(w(x))
, b(r(x)) -> r(b(x))
, b(w(x)) -> w(b(x))}
StartTerms: basic terms
Strategy: innermost
1) 'Fastest' proved the goal fastest:
'Fastest' proved the goal fastest:
'Bounds with minimal-enrichment and initial automaton 'match'' proved the goal fastest:
The problem is match-bounded by 1.
The enriched problem is compatible with the following automaton:
{ w_0(2) -> 1
, w_1(2) -> 3
, r_0(2) -> 2
, r_1(3) -> 1
, r_1(3) -> 3
, b_0(2) -> 1
, b_1(2) -> 3}
Hurray, we answered YES(?,O(n^1))